All of the 4th grade teachers and students from Almond went on a field trip to an art museum. Tickets were $$6.00$ each for teachers and $$4.50$ each for students, and the group paid $$69.00$ in total. The next month, the same group visited a science museum where the tickets cost $$24.00$ each for teachers and $$11.50$ each for students, and the group paid $$211.00$ in total. Find the number of teachers and students on the field trips.
Explanation: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${6x+4.5y = 69}$ ${24x+11.5y = 211}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-4$ ${-24x-18y = -276}$ ${24x+11.5y = 211}$ Add the top and bottom equations together. $ -6.5y = -65 $ $ y = \dfrac{-65}{-6.5}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $ {6x+4.5y = 69}$ to find $x$ ${6x + 4.5}{(10)}{= 69}$ $6x+45 = 69$ $6x = 24$ $x = \dfrac{24}{6}$ ${x = 4}$ You can also plug ${y = 10}$ into $ {24x+11.5y = 211}$ and get the same answer for $x$ ${24x + 11.5}{(10)}{= 211}$ ${x = 4}$ There were $4$ teachers and $10$ students on the field trips.